It made perfect sense at the time. When the Mission Bay neighborhood was just starting to fill in the vacant lots near AT&T Park, the San Francisco Unified School District asked an analyst for a projection. How many kids would live in the emerging development?

The short answer: not many.

“It was a reasonable assumption,” says school board member Rachel Norton. “Most of the housing is apartments (and condominiums), one- and two-bedrooms with a high price point. The thinking was couples might move in and have their first baby, but may not stay. They’d want a backyard or a third bedroom.”

Perfectly logical. Mission Bay is one of the few start-from-scratch neighborhoods in the city. Before the ballpark was built in 2000, it was empty space and abandoned warehouses. It has only been in the past 10 to 12 years that housing has filled in the open area between AT&T and the UCSF campus.

And then came story time.

When the Mission Bay Public Library branch opened in 2007 the staffers started a program reading stories for toddlers, figuring it would be a way to engage with nearby residents.

Frankly, there weren’t high hopes. As children’s librarian Ruben Balderas says, even the layout of the library seemed to imply that there wouldn’t be many kids.

“If you have been to our branch, the children’s area seems very, very small,” he said.

What no one expected was stroller gridlock. Story time, which is now staged twice a day three days a week, may be the hottest ticket in San Francisco.

For starters, this is reservation-only. Parents must sign up six days in advance to get one of the 55 spots for each of the two daily sessions. Registration begins the moment the library opens, and it is, well, chaos.

Parents are allowed to sign up either by phone or online. The ringing begins the minute the library opens, and staff can barely keep up on two phones. With two sessions a day, it works out to 55 people a session, or 110 a day. But you’d better move quickly.

All the spots are booked by phone within six to seven minutes.

“The other day someone was showing me that they tried to call 30 times and got a busy signal,” Balderas said. “In the last few months, it has just gotten crazy.”

So maybe online would be a better option? Not likely. Balderas says if you don’t book a spot within the first minute, you’re typically out of luck.

So, to review, if you want to attend Tuesday’s Toddler Tales or Thursday’s Baby Rhyme Time, you have to sign up six days in advance, and you have a window of roughly six minutes to book a reservation.

But what if you didn’t get in? There’s always standby in case someone failed to show up to claim the spot they reserved.

But you’d better get there early. Balderas says parents (and nannies) line up outside the library in the hope that someone fails to show up. It has reached the point that the library staff hands out tickets to those in line.

“There are people lined up before we open,” Balderas said. “We open at 10. I arrive at 9, and I’ve seen people lined up when I get here.”

It’s a cute story, but there are larger ramifications. For starters, this is clearly an extremely engaged neighborhood — maybe too engaged. At the end of February, a father, fed up with the fact that the new, very cool Mission Bay Children’s Park is still fenced off because of construction, used bolt cutters to cut open the fence.

In no time there were 50 parents and kids in the yard. Security ordered them out, but again, this is not a community that sits idly by when their kids are concerned.

And, by the way, the neighborhood is still growing. The 267-unit Arden condominium complex just opened, and it’s next door to the new Azure apartment complex with 273 units.

Hundreds of new units are already in place, and more are about to open. And that doesn’t include the proposed Warriors arena and the Giants’ planned mixed-use development south of the ballpark.

It’s a unique space in some ways. Realtors have begun referring to Mission Bay as the suburbs of San Francisco. The promotional brochure for Arden promises that residents can “escape the city without leaving.”

But now that the upscale demographic has moved there, they expect amenities. For instance, there’s no elementary school nearby. Two schools — Bessie Carmichael, a K-8, and Daniel Webster, a K-5 — are 30-minute walks away, according to Google Maps.

Residents have begun to advocate for a Mission Bay school, and the school district is listening.

“The positive in all this is that we have this group of engaged urban professionals,” Norton said. “There’s a lot of advocacy going on.”

The question, of course, is whether the families will stay. As always in San Francisco, there’s the problem of the third bedroom. Two-bedroom, two-bath units are fine for a couple with one child, but if they have a second, it gets crowded. And three-bedroom units are scarce.

It will also be interesting to see how this deeply involved parent group will react to the city’s confusing school lottery system. If they truly think of themselves as suburban dwellers in the city, they may well expect to be able to attend a school in their neighborhood.

But that’s all in the offing. For now the key is that, unlike what was expected, Mission Bay is a place for kids.

It’s only been in the last couple of years that we’re seeing confirmation of this trend,” Norton said. “We now know that they have a lot of kids, and they’re staying.”